Applications of concentration inequalities for statistical scoring and ranking problems

Abstract

In this overview paper, we consider the scoring approach applied to the ranking problem from a nonparametric perspective. We first focus on the problem of ROC curve optimization in terms of description of optimal elements. Then, we introduce summaries of this function-valued description of performance which are related to well-known statistics that are of higher order compared to averages of i.i.d. random variables. Eventually, we consider consistency and fast convergence results that rely on applications of concentration inequalities which involve U- and R-processes. This is a joint work with Stéphan Clémençon, Marine Depecker, Gábor Lugosi, and Sylvain Robbiano.